the Pressure of Radiation, 163 



Thus from {il'2)^ (27), and (29) we find that the mechanical 

 bodily force has a mean vahie oiven by 



Integrating from x = to x — oo, we see that the total 

 force per unit area is given by 



F=yJ^{1 + "'(1+^-^)}C-' (31) 



If E be the mean density of total energy, electric and 

 magnetic, of the vibrations to the left of the surface, we have 



E=,^^^(A^ + B^) (32) 



And from equations (28) we find 



F = E. (33) 



§ 6. Regarding then, as we have done, the pressure of 

 radiation as an integrated mechanical effect which only sums 

 up to a finite quantity on the average when there is ab- 

 sorption, we find that this pressure is equal to the mean 

 density of energy in front of the surface whatever be the 

 values of n and h for the medium provided the latter is not zero. 

 If the medium is perfectly transparent, the forcive is wholly 

 periodic, and has no effect on the aA^erage. The result also 

 holds for a plate of any medium if the thickness and the 

 value of h are Sfj related that the vibrations are practically 

 extinct before reaching the second surface ; and, of course, it 

 holds for the limiting case of perfect reflexion to which we 

 may approximate by supposing k to increase indefinitely. 



§ 7. By considering only the average effect of the forcive 

 to be measurable as mechanical pressure, we avoid some diffi- 

 culties in the thermodynamic applications ; for regarding the 

 pressure in front of a perfectly reflecting wall as periodic 

 with double the period of the radiation, Wien * has sug- 

 gested a violation of the Second Law by supposing the wall 

 to vibrate with the period of the pressure. In any case this 

 exception to the Law would be of the same order as Maxwell's 

 sugg"ested violation. 



§ 8. It is interesting to compare the result in (33) with 

 that given in (16) . In the case of the vibrating string there 

 is only one medium ; but in electrical radiation we have two 

 media to consider, the continuous aether and the material 



* Wien, Wied. Ann. lii. p. 150 (1891). 

 M2 



